A comparison of two parametric ROC curves estimators inbinormal model

The receiver operating characteristic curve ROC(t) plays an important role in many economic branches when it is necessary to classify between two populations. There are several approaches how to estimate it: classical estimator based on the empirical CDF, the weighted regression estimator, the estimator based on the best unbiased CDF estimator, non-parametric approaches based on the kernels or bootstraping. In the contribution the binormal model is considered and the attention is concentrated on the comparison of two parametric methods. The first one is the method of reweighted least squares where weights depend on the response variable. The second one is based on the best unbiased CDF estimator. The comparison of both methods will be demonstrated by simulations and the performance of both methods will be discussed for small sample sizes.